Name of the investigation: CHEERIO! - a probability game
Grade level: 6th or 7th grade
Approximate time frame for the investigation: One 50 minute period
Summary of investigation: Students will explore experimental and theoretical probability by playing a game of CHEERIO! The object of the game is to guess how often the sum of two numbers occurs when a pair of dice is rolled. First students determine the likelihood of rolling each sum by conducting an experiment. Then they use their knowledge of theoretical probability to determine the likelihood of rolling each sum mathematically. At the conclusion of this lesson, students make connections between experimental and theoretical probability by assessing their similarities and differences. Students will learn how to use probability to make predictions about future events. Students will learn how to interpret the relationship between experimental and theoretical probability.
Rationale and Relationship to Standards:
Concept 1: Students will be able to find and interpret the experimental probability of an event.
Relevant standard:CCSS.MATH.CONTENT.7.SP.C.6
Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.
Concept 2: Students will be able to find and interpret the theoretical probability of an event.
Relevant standard:CCSS.MATH.CONTENT.7.SP.C.7
Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
Relevance to Students’ Lives: This content is important for my students because understanding probability will help them in their future real world decision making such as whether they should study for the next math test, given the likelihood of getting an ‘A’, whether they should apply to a certain college, given the likelihood of being accepted, or whether they should buy a lottery ticket, given the chance of winning, etc.
Description:
List of materials: game board, 12 Cheerios per student, 1 pair of dice for each group of 4 students, probability worksheet for CHEERIO! game
Set-Up: The teacher will need to provide Cheerios, pairs of dice for every four students and copies of the game board and probability worksheet. The teacher will need to distribute all of these materials. The teacher will also need to determine the appropriate groupings since the game will be played together by four students.
What is expected of the teacher: The teacher will act as a facilitator, monitor student work and answer student questions.
What is expected of students: Students will participate in the CHEERIO! game as instructed on the probability worksheet. They should play two rounds of the game and complete the worksheet.
Step-by step instructions:
The teacher will distribute a bag of Cheerios along with a worksheet for the inquiry activity that includes a game board and instructions. She will introduce the inquiry activity and briefly give students some instructions – students will play a game called CHEERIO! which will give them an opportunity to apply what they have learned about probability.The game will serve as an experiment to help students determine how often the sum of two numbers occurs when a pair of dice is rolled. Students will use their results to calculate the experimental probability of rolling each sum.
Four students will play the game together. Each of them should take 12 Cheerios and place them under the numbers listed on their game board. They can place them all under one number, or spread them out however they like.
One student should volunteer to be the dice-roller .The dice-roller will roll a pair of dice, and then call out the sum of the two numbers rolled. If as student has a Cheerio underneath the number that is called out, he/she should take it off the game board. If he/she has more than one Cheerio underneath that number, he/she should only remove one of them. Using the probability worksheet, each student should record the sum on their frequency table for Round 1. Note: the sum should be recorded on the frequency table even if there isn’t a Cheerio on that number.
The dice-roller will continue to roll the dice and each player continues removing Cheerios one at a time until one person empties their board. Everyone continues recording all the sums rolled on their frequency tables for Round 1.
The first person to remove all of their Cheerios wins!
Student teams should play 2 rounds. Each student can place their Cheerios under different numbers in the 2nd round.
After students have finished play the game, they should calculate the experimental probability for both rounds (in total) and answer the Part I questions on the worksheet in preparation for a class discussion.
The teacher will ask students to share the results they obtained from the game/experiment.
For the next part of this activity, students will calculate the theoretical probability of rolling each sum using mathematical calculations.
Students should follow all of the instructions on the probability worksheet so they know how to properly calculate theoretical probability.
After students have finished their calculations, they should answer the Part II questions on the handout in preparation for a class discussion. Students will be asked to compare their experimental probability with their theoretical probability and note their differences.
The teacher will ask students to share their results.
LT 1: Students will understand the relationship between theoretical probability and experimental probability. (Concept)
Evidence: Students will be asked to explain the similarities and differences between experimental probability and theoretical probability on their worksheet. If students are able to write a clear explanation, then I will know that this target is being met.
Assessment: For LT1, which is a concept target, I will use a short essay as my assessment method.
LT 2: Students will be able to find and interpret the experimental probability of an event. (Practiced Skill)
Evidence: Students will be asked to complete a worksheet that requires them to calculate experimental probability. If they have most of the problems correctly completed, then I will know this target is being met.
Assessment: For LT2, which is a practiced skill target, I will use a selected response (short answer) assessment as my method.
LT 3: Students will be able to find and interpret the theoretical probability of an event. (Practiced Skill)
Evidence: Students will be asked to complete a worksheet that requires them to calculate theoretical probability. If they have most of the problems correctly completed, then I will know this target is being met.
Assessment: For LT3, which is a practiced skill target, I will use a selected response (short answer) assessment as my method.
CHEERIO!
Overview:
Rationale and Relationship to Standards:
Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.
Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
Description:
Assessment: